The objective of this paper is to show that under some
circumstances, the sign of a sampled sinusoid sequences, briefly
􀀀, is optimal to provide maximum energy transfer to linear resonators
in the context of discrete-time pulsed actuation at periodic
times with bounded sequences. It will be proven that there is an
optimal 􀀀 sequence which maximizes the resonator amplitude at
any given finite time, and that under some conditions, there is a
sufficiently high time above which any 􀀀 sequence at the resonant
frequency of the resonator also provides a locally unique maximum,
in the case of a lossless or leaky resonator. The tool used to
prove this last result is a theorem of quadratic programming. Since
pulsed digital oscillators (PDOs) under certain conditions produce 􀀀 sequences, a variation of the standard PDO topology that simplifies these conditions is also proposed. It is proved that except for
a set of initial conditions of the resonator of zero Lebesgue measure, the bitstream at the output of this topology produces a locally unique maximum in the total energy transferred to the resonator.